Equations and inequalities are in a class of expressions called relations.  In Derive a relation consists of two expressions separated by a relational operator.  The following table summarizes the relational operators and the one or two characters required to type in the operator on the expression entry line.  

=        =        equal operator

≠        /=        not equal operator

<        <        less than operator

≤        <=        less than or equal operator

>        >        greater than operator

≥        >=        greater than or equal operator


The relational operators can also be entered by clicking on them on the math symbol toolbar.  The relational operators are binary infix operators.  Thus to enter a relation, enter the left operand, the relational operator, and then the right operand.


The Simplify commandsSimplify_commands independently simplify the left and right sides of top-level equations.  For example,

x + 2·x = c + x·x

simplifies to

       2     
3·x = x  + c 


However, the Simplify commandsSimplify_commands simplify inequalities and non-top-level equations to a logically equivalent form with constants on the right and variables on the left. For example,

2·x + 3 < 5

simplifies to x<1.


Use the Solve commandsSolve_commands to solve individual or systems of equations and inequalities for one or more variables.  For example,

SOLVE(x + 2·x = c + x·x, x)

simplifies to

     3 - √(9 - 4·c)           √(9 - 4·c) + 3  
x = ————————————————  ∨  x = ———————————————— 
            2                        2        


Alternatively, you can solve equations and inequalities in a step-by-step manner for pedagogical reasons (see Step-by-Step Equation SolvingStep_by_Step_Equation_Solving).


Relations are not automatically regarded as simultaneous facts, and they are not automatically tested for truth or consistency.  Think of a Derive worksheet as a blackboard containing relatively independent expressions, including relations.  Some of these expressions may be derived from earlier ones.  However, others may have no relation to each other.  Variables may mean different things in different parts of a problem or a set of problems.  You can choose to combine subsets of these expressions (see Entering Mathematical ExpressionsEntering_Mathematical_Expressions), while ignoring other perhaps contradictory expressions.


Other Built-in Functions and ConstantsBuilt_in_Functions_and_Constants 

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